Thermal Expansion Questions and Answers

18 If a piece of metal is heated to temperature and then allowed to cool in a room which is at temperature 00 The graph between the temperature T of the metal and time t will be closed to

Fig 4 1 shows a Galilean thermometer This thermometer is used to measure the approximate temperature of the surrounding air glass cylinder water entia bulb E label 28 C bulb D label 26 C bulb C label 24 C bulb B label 22 C bulb A label 20 C Fig 4 1 The glass cylinder contains water When the temperature of the water changes so does its density Each bulb has a label printed with a temperature as shown in Fig 4 1 The bulbs have different densities At 21 C only bulb A is at the bottom of the cylinder a Explain in terms of density why bulb A is at the bottom of the cylinder and the other bulbs are floating

Two students carry out different experiments to compare the abilities of different metals to conduct thermal energy heat metal bar ABC D melted wax strip length of melted wax strip experiment 1 experiment 2 in experiment 1 the bar is heated for one minute and the length of wax strip that melts is measured decreases decreases In experiment 2 the bar is heated and the time taken for the pin to drop off is measured What happens to each of these measurements when a better conductor of thermal energy is tested increases 1 heat increases metal bar time taken for the pin to drop decreases increases decreases increases wax pin

The pressure applied from all directions on a cube is P How much its temperature should be raised to maintain the original volume The volume elasticity of the cube is and the coefficient of volume expansion is a Question Type Single Correct Type 1 2 P a Pa B PB

Consider a hydrogen like atom whose energy in nth exicited state is given by En 13 6 Z2 n when this excited atom makes a transition from excited state to ground state most energetic photons have energy Emax 52 224 eV and least energetic photons have energy Emin 1 224 eV The atomic number of atom is a 2 c 4 b 5 d None of these

anal area A 100 C and ductivity of stance from the middle ached Variation of density corresponding variation in its volume is as shown questions Temp C 1 Both graphs have been correctly plotted 2 Both graphs have been incorrectly plotted 3 Only variation of density is plotted correctly 4 Only variation of volume is plotted correctly Space for Rough Work T C

Q 1 SINGLE CHOICE One mole of an ideal gas is contained under a weightless conducting piston of a vertical cylinder at a temperature T The space over the piston is open to the atmosphere The amount of work that has to be done to increase the gas volume in the cylinder to n times by slowly raising the piston is Neglect friction T H d 3IG f Talu UR 3 afe a7 i HT 34 62 31 Mz27 WA MA 42 1 EAZ AZ FAZZA da ch nya ac d fa f g u c anvq ma 1 A a C RT n 1 ln n Correct Answer BRT n 1 In n RT n 1 2 2 In n 1

A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated P by the metal The sensor has a scale that displays log2 P Po where Po is a constant When the metal surface is at a temperature of 487 C the sensor shows a value 1 Assume that the emissivity of the metallic surface remains constant What is the value displayed by the sensor when the temperature of the metal surface is raised to 2767 C 2016

An idealized diesel engine operates in a cycle known as air standard diesel cycle as shown Fuel is sprayed into the cylinder at the point of maximum compression B Combustion occurs during expansion BC P B C A B C D Adiabatic Process D A V Heat is absorbed during process BC Heat is released during process DA Heat is absorbed during process CD Efficiency of the cycle is 1 To TA

Three rods of equal length are joined together and clamped at their ends as shown in the figure The upper and lower rods are identical a Y and the middle one is of different material Y Find the final length of the system if the temperature is increased from T to T Consider no bending and a d 1 Y a2 Y a Y

A cylindrical block of wood floats vertically with 80 of its volume immersed in a liquid at 0 C When the temperature of the liquid is raised to 62 5 C the block just sinks in the liquid The coefficient of cubical expansion of liquid is A 1 10 K 1 B 2 10 K 1 C 3x10 K 1 D 4 10 K 1

liquid w The coefficient of apparent expansion of a determined using two different vessels A and B are 7 Y2 respectively If the coefficient of linear expansion of vessel A is a the coefficient of linear expansion of the ve EAMCET 2000 B is a c ay1 2 71 72 71 72 a 3 b d 71 72 2a 71 72 3 a

Two strings of the same length but different mass per unit length are used to suspend a rod whose density varies as p po 1 ax as shown in the figure The frequency of standing waves produced in the string is in the ration 1 when both the strings are vibrating in their fundamental mode If the mass per unit length of string 1 is o calculate the mass per unit length of the other string alus for the rod Y and density p 1 L 2 f

A metal block is volume expansion coefficient y kept on rigid horizontal surface as shown in figure Initially temperature of the block is same as the surrounding Now AQ amount of heat is given to the block If mass of the block is m specific heat capacity of the metal is s then AQ A Temperature of the block increases by amount mis AQ ms B Temperature of the block increases by amount slightly less than C Work done by block on atmosphere is positive D Work done by gravitational force on block is positive

A sphere made of polymer is floating on the surface of water which is at a temperature of 20 C and 1 of the volume of the sphere is above the water To what final temperature in C must the water be heated in order to submerge the polymer sphere completely Take coefficient of linear expansion of the polymer 2 30 10 5 C and coefficient of volume expansion of water 3 19 10 N PC If your answer is N fill value of 20

A barometer gives correct reading at any temparature and coefficient of linear expansi scale glass tube are a b and coefficient of real expansion of mercury is c Then 1 C a12b 2 c a b 3 c 2a b 4 c 3a 3b

Two rods of same mass are made up of different materials having specific heat in the ratio 3 4 and coefficient of linear expansins in the ratio 2 5 When they are supplied by same heat their linear expansions are equal Find ratio of their original lengths 1 15 8 2 3 10 3 8 15 10 3

The ends of the bars shown in the figure are 5 mm apart at 25 C The left hand bar is brass and is 1 00 m long and the right hand bar is steel and is 1 00 m long as well assuming the outer ends of both bars are firmly supported against rigid supports a Determine at what temperature the ends of the facing bars just touch b If only 5 um were separated what would now be the necessary temperature to join them

he temperature of a disk made of a certain metal is increased to 100C The radius of said disk increased by 0 22 Calculate the percentage increase of 1 The surface of the disc face 2 Disc thickness 3 Disc volume 4 The mass of the disk Also calculate e the coefficient of linear expansion

Stress strain graph for a metallic wire is shown at four different temperatures T T T3 and T4 Choose the correct option Stress T 1 O T T2 T3 T4 O T T T3 T4 O T T T3 TA T3 T2 T TA T T T Strain

Variation of radiant energy emitted by sun filament of tungsten lamp and welding arc as a function of its wavelength is shown in figure Find t correct match option from the following E T3 T Sun T tungsten filament T3 welding arc T Sun T3 tungsten filament T2 welding arc T Sun T tungsten filament T welding arc T3 Sun T tungsten filament T2 welding arc T3

sec ERA op Manto A metal bar of length and area of cross section A is clamped between two rigid vertical supports The Young s modulus of rod is Y and coefficient of linear expansion is a Find the force exerted by the rod on the support if temperature of rod is increased by At C 1 3 YAAtl YA At 2 YalAAt 4 YAast 9 10 2028 Seen r The ler percentage incre ratio of wire mate C 1 0 3 3 0 27 A mass of 3 kg of area 10 cm gas Find the fr sphere if its bu placed in the gi 1 0 5

Two wires of equal length and cross section area suspended as shown in figure Thier Young s modulus are Y and Y respectively The equivalent Young s modulus will be 1 Y Y Y Y 3 Y Y Y Y 4 Y Y

7 A copper wire is held at the two ends by rigid supports At 50 C the wire is just taut with negligible tension If Y 1 2 10 1 N m a 1 6 x 10 5 C and p 9 2 x 103 kg m then the speed of transverse waves in this wire at 30 C is 1 64 6 m s 3 23 2 m s 2 16 2 m s 4 32 2 m s

The resistance of a metal increases with increasing temperature because VITEEE 2008 a The collisions of the conducting electrons with the electrons increase b The collisions of the conducting electrons with the lattice consisting of the ions of the metal increase c The number of conduction electrons decreases d T her of conduction electrons increases

11 In a practical application of flexural formula SSB carrying UDL w per unit length on the entire span The maximum bending moment will be equal to WL 2 8 WL 8 O WL 4 OWL 12 Refer data in example 13 What is the value of average shear stress O 0 43 N mm 2 O 120 N mm 2 O 9200 N mm 2 O 0 65 N mm 2

A brass rod and an aluminium rod each of length 1 m and same cross section area 1 cm are placed in contact with each other as shown Temperature of both the rods is raised by 100 K The coeffcients of linear expansion of brass and aluminium are 2 0 x 10 5 K 1 and 2 4 x 10 5 K 1 respectively If the Young s moduli of brass and aluminium are 1011 N m and 7 x 1010 N m respectively then stress in the rods is Brass 1 1 1 x 106 N m 3 1 8 x 108 N m Aluminium 2 1 5 106 N m 4 2 0 x 108 N m

A steel rod of radius 2 4 cm the ends of which are fixed is subjected to a tensile force of modulus 19 kN at both ends What is the stress if the temperature a drops by 14 degrees answer x10 PA B rises 14 degrees The Young s modulus of steel is 2x 1011 N m The mantissa of the result must be in the interval 1 10

This shows that n depends only upon T and T i e independent of working substance For 100 efficiency T must be OK i e the temperature of the sink must be at absolute zero Since this is impossible attaining 100 efficiency is impossible When T T we have n 0 i e the engine does not work Example 11 Calculate the efficiency of an engine that absorbs heat at 600K and exhausts it at 400K Solution T 600K T 400K Efficiency T T 600 400 600 n T n 26 6 11 13 X 08

c The temperature of an ideal gas at initial pressure P and volume V is increased isochorically until the pressure is doubled The gas is then expanded isothermally until the pressure drops to original value Then it is compressed isobarically until volume returns to initial value Sketch this process in the P V and P T plane Calculate the total work done if n 2 kilomoles P 105 Pascal V 2m 6

2 moles of He are mixed with 2 moles of H in a closed adiabatic container Initially the mixture occupies 3 litres at 27 C The volume 3 is suddenly decreased to times Choose the 2 correct option s He and H can be treated as ideal gas y for mixture is 312 Final temperature 300 2k

b Consider that an ideal gas initially confined in a volume at any given temperature is allowed to expand and the whole arrangement is thermally insulated Is it possible not to have any thermodynamic work even though there is expansion in its volume Justify your answer and give an example Find the entropy change of an ideal gas undergoing such a process 8 75

22 A horizontal uniform tube open at both ends is containing a liquid of certain length at some temperature When the temperature is changed the length of the liquid in the tube is not changed If a is the coefficient of linear expansion of the material of the tube and y is the coefficient of volume expansion of the liquid then EAMCET 2013 d y a a y 2a b y 3 a c y 4 a

unit 100K T 1000 K where T is the For a 2 m long rod at 127 C the linear expansion coefficient is a T temperature of rod in Kelvin Find the final length of rod if its temperature increased from 127 C to 527 C B 2 5 m 4m 3m None of these C

40 r 11 A substance having coefficient of critical expansion 4 9x 10 4 C The fractional change in the density 2 for the rise in temperature 30 K is UP CPMT 2015 d 0 0145 a 0 0012 b 0 1280 c 0 0235 12 At constant pressure the ratio of increase in volume norature

4 The length of a steel rod is 5 cm longer than that of a brass rod If this difference in their lengths is to remain the same at all temperatures then the length of brass rod will be coefficient of linear expansion for steel and brass are 12 10 6 C and 18 x 10 6 C respectively a 20 cm b 15 cm c 5 cm EMACET 2015 d 10 cm

Diagram shows the variation of potential energy with separation between the two atoms for three different substances All the objects are nearly at absolute zero temperature Choose the correct statement s 1 Substance A NEN parabola Substance A expands on heating Substance B contracts on heating Substance C contracts on heating Substance B neither expands nor contracts on heating Substance B Substance C

A copper rod 2 m long has a circular cross section of radius 1 cm One end is kept at 100 C and the other at 0 C and the surface is covered by non conducting material to check the heat losses through the surface The thermal resistance of the bar in degree kelvin per watt is Take thermal conductivity K 401 W m K of copper 12 9 13 9 14 9 O 15 9

Two straight metallic strips each of thickness t and length L are nveted together Their coefficient of inear expansions are a and dp If they are heated through temperature AT the bimetallic strip will bend to form an arc of radius proportional to a1 0 AT 1 01 0 AT 0 0 T NODE

The coefficient of thermal conductivity of copper is nine times that of steel In the composite cylindrical bar shown in the figure what will be the temperature at the junction of copper and steel 100 C 1 75 C 3 33 C 18cm copper iron 0 C 6cm 2 67 C 4 25 C

The ends Q and R of two thin wires PQ and RS are soldered joined together Initially each of the wires has a length of 1 m at 10 C Now the end P is maintained at 10 C while the end S is heated and maintained at 400 C The system is thermally insulated from its surroundings If the thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is 1 2x10 K the change in length of the wire PQ is UJEE Advanced 2016 0 78 mm 0 90 mm 1 56 mm 2 34 mm

Which of the following circular rods given radius r and length each made of the same material as whose ends are maintained at the same temperature will conduct most heat CBSE PMT 2005 AFMC 2006 r 2ro l 210 r 2ro l lo r roil lo r ro l 210 2

Six identical metallic rods are joined together in a pattern as shown in the figure Points A and D are maintained at temperature 60 C and 240 C The temperature of the junction B will be DUMET 2010 120 C B 150 C 60 C 80 C C D

Change in length of a solid when it is heated depends O a Change in temperature O b Neither original length nor change in temperature O c Original length and Change in temperature O d Original length

Two rods A and B are of equal lengths Their ends are kept between the same temperature and their area of cross sections are A and A2 and thermal conductivities K and K The rate of heat transmission in the two rods will be equal if CBSE PMT 2002 NEET Karnataka 2013 K A K A1 K A K A2 K K K A K A

If the temperature difference on the two sides of a wall increases from 100 C to 200 C its thermal conductivity MP PMT 2006 Remains unchanged Is doubled Is halved Becomes four times

The pressure at the bottom of a water tank is 4P where P is atmospheric pressure If water is drawn out till the water level decreases by 3 5th then pressure at the bottom of the tank is

Two lines AC and BC are drawn on a circular disc as shown in figure The disc is made of a material with linear expansion coefficients a a Here a and a are linear expansion coefficient for expansion in x direction and y direction respectively C is the centre of disc If the disc is heated uniformly Angle ACB 0 will A increase B decrease C remains constant D may increase or decreases depending on value of temperature increment

Two rods of material X sandwich another rod of material Y as shown in Figure Rivet X Y X Rivet L At temperature T the three rods are in a state of zero strain have length L and are riveted to each other If the temperature of the system increases to T AT find the final length of the system of the three rods Given that the coefficients of linear expansions of the rods are a and Young s modulus for material X is Y and that

3 Two identical uniform rods A and B are of equal length L and have same temperature The cross are square with edge length a Rod A is kept over a smooth surface while the rod B is kept on a rough surface with coefficient of friction Mass of each rod is m and coefficient of liner expansion is a L L A Smooth Rough Heats are given to both the rods and temperatures are increased Rise in temperature is same for both the rods given by AT Work done by weight mg of the rod A during expansion is en boi 2 4 1 mg AT 2 3 a mg 1 AT 2 B a mg AT 2 a mg 1 0 AT